Those are not regular Slobber straps. They are for use with barrel racing reins that have a hole bored through the rein itself. YOu pull the thong out of one side of the slobber strap, but the rein in between the two sides of the Slobberstrap (sandwiched) and wrap it around the bit rings, and lace the thongs through the rope reins and then through the slobber strap (from inside to outside) and then tie them off.
OR, you run the rope reins through the big openning (the bit will also go through that openning) and then back on themselves a few inches and then used thread or whatever, wound around the rope rein and the doubled back portion to tie the doubled back portion to the main rein.
For the most part, the first explanantion is how I have seen them used. Not with a true mecate but with barrel reins that have the laces actaully going right THROUGH the rope.